Bound Definition and 476 Threads

Transition from bound states to "continuous" states If I have the Hamiltonian for the Hydrogen atom and a perturbation given by a classical electric field (the kind of problems you get in an ordinary course about QM, no QFT involved), can I have a transition from a bound state (I intend a...

Hello, I'm reading Griffiths' Introduction to Electrodynamics and I got quite confused in 9.4.1 page 392 (but the question is general, for anyone who does not have that book): It's about EM-waves in conductors. I will quote a paragraph: What is the definition of bound (or free)...

[PLAIN]http://img96.imageshack.us/img96/7816/12530747.jpg Hopefully this will post successfully... Erm its the first part I'm not sure on, after that it's easy. I'm just not understanding the wording. I need to work out the effective green time during the cycle

Homework Statement Rotate the area bound by the following lines around the x-axis. y = x^2+1, y = -x^2+2x+5, x = 0, x = 3 Homework Equations None that are uniform enough to put here considering I'm fairly sure it's not washer... The Attempt at a Solution

Homework Statement Prove: The set S(V) of all subspaces of a vector space V is a complete lattice under set inclusion, with smallest element {0}, largest element V, meet glb(S_{i} | i \in K) = \cap_{i \in K} S_{i} and join lub(S_{i} | i \in K) = \sum_{i \in K} S_{i} (Btw, how can I write...

Had a recent homework questions: Find a bound for the error |f(x)-P3(x)| in using P3(x) to approximated f(x) on the interval [-1/2,1/2] where f(x)=ln(1+x) abd P3(x) refers to the third-order Taylor polynomial. I found the Taylor series of f(x) seen below: x- x^2/2!+(2x^3)/3! I know...

Effective theory of bound states from QCD?? Do you know any work that actually succeeds in producing the action of an effective field theory for nucleons and mesons, starting from the QCD action?

Find the area bound between y2 = x + 5, and y2= 3 - x.I can't figure out how to put limits of integration, the integrand, or really anything besides just the integral sign to work with Latex, so bear with me (or better yet, direct me to a tutorial! I will search for one after this post, if there...

So I'm kind of new to the whole physics thing so be nice please :P If i guess "nature" keeps objects from being able to go the speed of light then does "nature" keep light from going slower/faster than that speed? I first thought of this when i read a thread asking if gravity actually...

Hello, I am trying to come up with an expression for a bound on the sum of higher order terms, above second order. Consider the following Taylor expansion of a function f(x) around a point a, f(x) = f(a) + \frac{f^{(1)}(a)}{1!}(x-a) + \frac{f^{(2)}(a)}{2!}(x-a)^2+...

I have been trying to remember if in classical EM it is equivalent to describe magnetization through bound electric currents A. \vec{j_b} = \nabla \times \vec M \vec{k_b} = \vec M \times \vec{\hat{n}} OR bound magnetic charges B. \rho_b = -\nabla \cdot \vec M \sigma_b = \vec M \cdot...

i proved that sin (1/x)<1/x prove that sup{xsin (1/x)|x>0}=1 if we say that A={xsin (1/x)|x>0} xsin (1/x)<x(1/x)=1 so one is upper bound now i need to prove that there is no smaller upper bound so that 1 is the supremum suppose that "t" is our smaller upper bound t<1 and...

Homework Statement I am solving some convolutions, and i have come to these solutions. a)\sum2k, summing from -\infty to -1 b)\sum2k, summing from -\infty to n , where n <=-1Homework Equations the geometric series summation formula, from 0 to N \sumak = 1-aN+1 / 1-a , summing from 0 to N The...

I am working on a proof in which I have an integral with bounds negative infinity to zero, with an even function, i.e., f(y) = f(-y). I took the limit to infinity rather than negative infinity since y is negative (which is OK I think) but now I have an integral that goes from infinity to 0. What...

I am trying to understand the following theorem: An ordered field has the least upper bound property iff it has the greatest lower bound property. Before I try going through the proof, I have to understand the porblem. The problem is, I don't see why this would be true in the first...

Homework Statement Find an upper bound M for f(x) = abs ( x+2 / x-8 ) if abs(x-7) < 1/2Homework Equations The Attempt at a Solution i first found set of x values using abs(x-7) < 1/2 which is 13/2 < x < 15/2. Now, i believe i have to find other set of x values to compare to find upper...

Question: If we assume that an electron is bound to the nucleus (assume a H atom) in a circular orbit, then the Coulomb force is equal to the centripetal force: mv^2/r= ke^2/r^2 In the Bohr hypothesis, angular momentum, L = mvr is...

Hi all! I hope this is the right section to post such a question... I'm studying the theory of resolvent from the QM books by A. Messiah and I read in a footnote (page 713) that the norm of the resolvent satisfies \|R_A(z)\| = \lVert \frac{1}{A-zI} \rVert \ge \text{dist}(z,\sigma(A))^{-1}...

Homework Statement LEt S is supset of real numbers and suppose that there is X0 is member of S such that x0>=x for all x which is member of S(i.e. x0 is the maximum of S). show that x0=supS Homework Equations The Attempt at a Solution Not: this seems too easy question but i...

Homework Statement Let (an) be a boundedd sequence, and define the set S= {x\in R : x < a_n for infinitely many terms a_n\} Show that there exists a subsequence (a_n_k)converging to s = sup S Homework Equations This is supposed to be a direct proof of BW using the LUB property, so no...

I am new to differential equations, any help would be great. I have a ODE of the second order u''x = e^x over the domain [1, 1] where u'(0) = 0 is a Neumann boundary on the ODE. I am trying to approximate the solution using the finite differences method, I can do Dirichlet boundaries with...

An electron in an orbital of an atom has some energy and some momentum. In some ways it can be considered "orbiting" but it is not really moving in a classical sense. I've heard more than once the explanation that electrons in high orbits move close to the speed of light and that this...

In hydrogen atom the electron and the proton come very close to each other statistically(their wavefunctions even merge), so why we do not see the effect of gravity which should be on the order of other forces at Planck distance. Otherwise, compton to compton wavelength distance is too high for QG.

Any reviews of this book? Any would be helpful!

Problem Statement: Prove that the least upper bound of a set of integers is an integer. Attempt: Using well ordered principle this is very trivial. However, is there another way? ANY comments or ideas relating to the topic would be highly appreciated. It is assumed that the set...

Partial Order/Upper Bound Proof from "How to Prove It" Homework Statement Suppose R is a partial order on A and B is a subset of A. Let U be the set of all upper bounds for B. Prove that U is closed upward; that is, prove that if x E U and xRy then y E U. Homework Equations N/A The...

Homework Statement 1. f(n) = n - 100 g(n) = n - 200 2. f(n) = log(2n) g(n) = log(3n) n >= 0 in all cases Find out if f(n) is an upperbound, lowerbound or both of g(n) Homework Equations The Attempt at a Solution in case of 1, f(n) has to be an upperbound of g(n) because...

Hello, I am learning very, very basic quantum from the internet, and I have a question about the reason why dineutrons cannot exist. I know that the standard answer is that they aren't bound, but I don't understand why they are not, whereas a proton-electron system is. Here is the context in...

Someone please tell me if I am thinking right: Let's consider an unperturbed electronic state of an atom/molecule. If we denote it by [a>, then the average electronic momentum in state [a> is, <p> = <a]p[a> = (<a]p<a])* (because p is hermitian) = (<a]*p*[a>*)...

Hey all. So, I understand that every bound electronic state will have zero average electronic momentum, because otherwise the electron will fly off the atom. But how do I show mathematically that < p > = 0 for any bound state. Any help or reference greatly appreciated. Thanks.

Hi, I'm trying to understand the quantum mechanical solution to this potential: V(x) = \left\{\begin{array}{cc}\infty & \mbox{ for } x < 0,\\-\lambda\delta(x-d) & \mbox { for } x > 0\end{array}\right. A particle of mass m is constrained to move on the half straight line \{x \in \mathbb{R}: x...

So, I have this problem I am tackling where I am doing a Bayesian scan of a multi-dimensional model. Most of the quantities predicted by the model have likelihood functions which are normal distributions (as functions of the possible data values), however there are some pieces of experimental...

Hi, I need help to determine the upper bound of this infinite series. \sum_{k=p+1}^{\infty} \frac{1}{k} a^k \ \ \ \ ; a \leq 1 The paper I am reading reports the upper bound to be, \sum_{k=p+1}^{\infty} \frac{1}{k} a^k \leq \frac{1}{p+1}\sum_{k=p+1}^{\infty} a^k = \frac{1}{p+1} \cdot...

Hi, I asked this question in the quantum physics forum https://www.physicsforums.com/showthread.php?t=406171 but (afaics) we could not figure out a proof. Let me start with a description of the problem in quantum mechanical terms and then try to translate it into a more rigorous mathematical...

Consider a uniform, isotropic , homogeneous solid dielectric slab. We know, induced surface charge=\overline{P}.\widehat{n} and \overline{P} \alpha \overline{E} So, as applied electric field increases, polarization per unit volume increases. which implies that surface...

Hi, I discussed this with some friends but we could not figure out a proof. Usually when considering bound states of the Schrödinger equation of a given potential V(x) one assumes that the wave function converges to zero for large x. One could argue that this is due to the requirement...

i have two questions that i am struggling with and i have tried all i can think of with them and i am still not getting the answers correct. 1)Estimate, using the Uncertainty Principle, the kinetic energy of an electron if it were bound in the nucleus. Answer: ∼ 200 MeV for R ∼ 1 fm...

Hi guys, just got owned by my calc prof with a final exam question. Very very weird. Attempted it and different approach apparently gets u different answers. I have no idea what's going on.. I have attached the question as a word document. Too much integration to type and I cannot really use...

Homework Statement Let \mathcal{F} \subset C(\mathbb{R}) be a set of continuous functions such that for each x \in \mathbb{R} there is an M_x > 0 such that |f(x)| \leq M_x for all f \in \mathcal{F}. Homework Equations Prove that there is a nonempty open subset Y \subseteq X and an M...

I have read in a book about bound vectors that we can not move them i mean that they can not move parallel to any location. Can someone please give me an example. Also if we are given two bound vectors, is it possible to find the dot and cross product of two vectors.

These days I met one problem and asked a professor for help. But I can not understand his answer. Can you help me explain his answer? My question is that whether we can assume that a plane wave is orthogonal to the bound state of Hydrogen atom when t->\infty? Professor answers...

ok. this is an easy enough thing to prove in one dimension but my question seems to be 3 dimensional and it's causing me some hassle: show the expectation value of the kinetic energy in a bound state described by the spherically symmetric wavefunction \psi_T(r) may be written \langle...

Homework Statement Estimate sin4 accurate to five decimal places (using maclaurin series of sin) Homework Equations The Attempt at a Solution Lagrange error bound to estimate sin4° to five decimal places( maclaurin series) 4°=pi/45 radians |Rn(pi/45)<1*(pi/45)^n+1/(n+1)...

Hello, Well, actually it's not a homework problem, I just got really confused about bound charges. Originally, I thought it was just a special technique to do the integral, but somehow Griffiths suggest that bound charges are phsically exist.(chap. 4.2.2) Well, I can accept his argument...

Find the total mass that occupies a solid region D bounded by a sphere of radius 3 centered at the origin and z = 1 if the density of the function is (x, y, z) = 1/1+x^2+y^2+z^2 . I would like to be able to do this problem using spherical coordinates but I am unsure about how...

How does one solve bound state problems in QFT(like an electron positron atom)? How does one identify the space of states. The Fock space seems to lose it definition when a bound state problem is discussed. There is also no meaning to wave functions or potentials that are used in standard...

Homework Statement I am given the following two functions: y=x3-13x2+40x and y=-x3+13x2-40x I need to find the area bound between the above two functions. Homework Equations Integrals! The Attempt at a Solution I don't know how to do this as there is 3 points of intersection...

My question: Should the sum of all bound currents always be zero? For example, should the bound currents of a cylinder with both bound volume current density and bound surface current density always sum up to zero? Does the uniformity of current ran through the cylinder have any effect...

Homework Statement The region bounded by the given curves is rotated about x = 10 x=1-y^{4}, x=0 Find the Volume V of the resulting solid by any method. Homework Equations The Attempt at a Solution I'm using the washer method. Not sure if it is being setup properly as I'm getting the...

Say you have a Yukawa potential (a.k.a. screened coulomb potential) V(r) = -\frac{e^2}{r}e^{-rq} where q is the inverse screening length, how would you find the critical q for having bound states? I'm working on reproducing N.F. Mott's argument about the critical spacing of a lattice of...